Socolar-Taylor Aperiodic Tile
by Gelada, published
A single tile that can fill three dimensional space but never gives a periodic tiling. For more details see:
A blender file with the python code constructing the model is here:
Use the model in a 3d printer.
Two models are provided. Copies of the actual tile cannot be fitted together without access to a 4th dimension. A simpler tile that does not have all the markings should fit together, but can also give periodic tilings.